An urn contains 3

Given: An urn contains 3 white and 6 red balls

To find: the probability distribution of the number of red balls drawn and mean and variance of the distribution

Let X denote the number of red balls drawn in four balls from total of 9 balls

X can have five value, i.e. 0, 1, 2, 3, 4 as there are 6 red balls

Now,

Probability of getting 0 red ball = P(X=0)

The probability of getting 1 red ball = P(X=1)

The probability of getting 2 red balls = P(X=2)

The probability of getting 3 red balls = P(X=3)

The probability of getting 4 red balls = P(X=4)

Probability Distribution Table

Formula used:

Therefore,